By considering the dynamics of the apparent motion of a stationary object relative to a moving observer, we construct a partial differential equation that relates the changes in an image to the motion of the observer. These come in two varieties: a first order system that describes the coevolution of the egocentric radial distances to objects and the visual scene, and a second order system that does not involve any distances or other geometry. The later equation leads, via the calculus of variations, to a novel technique for recovering egomotion from image sequences, a so-called visual yaw detector, which is tested on real data. For expository purposes the derivation is carried out in two dimensions, but the approach extends immediately to three.